Bake meatballs in the preheated oven until browned and center is no longer pink, 3 to 4 minutes per side. Turn the tray around once to be sure the meatballs roast evenly; flip meatballs halfway through cooking.

Bring a large pot of lightly salted water to a boil. Cook mini penne in the boiling water for about 5 minutes, stirring occasionally. Add spinach and continue cooking until pasta is cooked through but firm to the bite, about 3 minutes more. Reserve about 1/4 cup pasta cooking water and drain remaining water.

Return pasta and spinach to the pot and stir in olive oil, Parmesan cheese, and reserved cooking water. Top pasta with meatballs before serving.